An edge computing system energy and task scheduling optimization method

Abstract

This invention relates to the field of the Internet of Things (IoT) and discloses an optimization method for energy and task scheduling in an edge computing system, comprising the following steps: First, based on a new energy and task scheduling protocol, the MEC system can adaptively switch between energy harvesting mode, IRS auxiliary task offloading mode, and IRS standby task offloading mode according to channel conditions, IRS battery energy state, and user task queue state; Second, based on the developed protocol, the system optimization problem is modeled to minimize long-term user task offloading and computing energy consumption; Third, using the Lyapunov optimization method, the problem is decomposed into a time-slot-based deterministic optimization problem, and the corresponding deterministic optimization problem is solved using convex optimization theory.

Description

Technical Field

[0001] This invention relates to the field of the Internet of Things (IoT), specifically to an optimization method for energy and task scheduling in edge computing systems. Background Technology

[0002] With the rapid popularization of the Internet of Things (IoT), an increasing number of IoT smart sensor nodes need to perform latency-sensitive, computationally intensive tasks. However, due to limited computing resources, completing these tasks locally on these nodes is often impractical or prohibitively expensive. As one of the emerging technologies in IoT, mobile edge computing (MEC) allows IoT nodes to offload their computational tasks to servers with sufficient computing resources, potentially offering an effective solution to these problems. Deploying MEC on IoT can not only reduce task execution latency but also save energy for IoT nodes. Therefore, designing high-performance MEC systems has attracted considerable interest from researchers in recent years.

[0003] Intelligent reflectors (IRS) are a cost-effective technology proposed in recent years for achieving high-spectrum-efficiency wireless communication systems. In wireless communication systems deploying IRS, adjusting the phase shift of the reflected signal from passive components on the IRS can improve the received signal power of the wireless receiver. In MEC systems, combining IRS technology can make task offloading more efficient, thereby achieving better system performance. Therefore, how to design IRS-assisted MEC systems has become a topic of great research interest to scholars in recent years.

[0004] Reference 1 [T. Bai, C. Pan, Y. Deng, M. Elkashlan, A. Nallanathan and L. Hanzo, "Latency Minimization for Intelligent Reflecting Surface Aided Mobile Edge Computing," IEEE Journal on Selected Areas in Communications, vol. 38, no. 11, pp. 2666-2682, Nov. 2020] studies the benefits of deploying an IRS in a MEC system, where multiple devices offload tasks to edge computing nodes via the IRS, with the goal of minimizing latency under edge computing capability constraints and IRS phase shift constraints.

[0005] Most existing studies assume that IRSs are powered by batteries or the grid, allowing phase shifts of passive components to be adjusted via controllers. However, replacing or recharging batteries is often expensive and inconvenient, and may even be impossible in harsh environments or special applications. Therefore, the lifespan of battery-powered IRSs is easily limited by battery capacity. If a fixed power supply is used, the IRS can only be deployed in locations with grid access, rendering it unusable in many situations without grid connection. Wireless radio frequency (RF) energy harvesting is a new technology that allows wireless nodes equipped with RF energy harvesting circuitry to extract energy from RF signals to extend their lifespan. Therefore, wirelessly powered IRS-assisted wireless communication systems incorporating RF energy harvesting technology have recently received widespread attention from researchers.

[0006] Reference 2 [S.Xu,Y.Du,J.Liu and J.Li,“Intelligent reflecting surface based backscatter communication for data offloading,”IEEE Trans.Commun., to be published, doi:10.1109 / TCOMM.2022.3170629.] assumes that the IRS is connected to the user terminal and helps the user terminal offload task data to multiple MEC servers for collaborative computing. The energy consumed by the IRS operation and the user's local computing is obtained from the RF signal emitted by the power beacon.

[0007] Reference 3 [S.Mao, N.Zhang, L.Liu, J.Wu, M.Dong, K.Ota, T.Lui, and D.Wu, “Computation rate maximization for intelligent reflecting surface enhanced wireless powered mobile edge computing networks,” IEEE Trans. Veh. Technol., vol.70, no.10, pp.10820-10831, Oct.2021.] assumes that the IRS and all user terminals are powered by energy harvested from the RF signals transmitted from the base station, and the IRS uses the harvested energy to assist the user terminals in offloading task data to the base station.

[0008] Problems with existing technologies: In existing studies, such as references [2-3], for the sake of simplifying the analysis, it is assumed that the computing tasks generated by the user end at the beginning of a time slot must be completed in the current time slot, and that energy scheduling adopts the collect-use strategy used by most wireless power supply systems, that is, the energy collected by the IRS in a time slot must be used up in the current time slot. However, the HTU method cannot increase the amount of energy collected within a limited time range and cannot effectively utilize the collected energy at the IRS end.

[0009] Based on the above analysis, a design scheme different from that in references [2-3] needs to be studied to increase the energy collected by the IRS and utilize the collected energy efficiently, thereby improving system performance. To this end, a new energy and task scheduling protocol is first proposed so that the MEC system can adaptively switch between three modes (i.e., energy collection mode, IRS-assisted task offloading mode, and IRS standby task offloading mode) according to channel conditions, IRS battery energy state, and user task queue state. In energy collection mode, the IRS can accumulate collected energy, which will be used in subsequent time slots; in IRS-assisted task offloading mode, the user terminal offloads task data to the HAP with the assistance of the IRS; in IRS standby task offloading mode, the IRS is in standby state (i.e., no longer using energy), and the user terminal only offloads task data to the HAP via a direct link.

[0010] Due to the randomness of wireless channels and task arrival, and the interconnectedness of system operating modes and resource allocation decisions in each time slot, the problem is a stochastic optimization problem of multi-stage sequential decision-making, which is difficult to solve directly. Therefore, we propose an optimization method for energy and task scheduling in edge computing systems. Summary of the Invention

[0011] (a) Technical problems to be solved

[0012] To address the shortcomings of existing technologies, this invention provides an optimization method for energy and task scheduling in edge computing systems, thus solving the aforementioned problems.

[0013] (II) Technical Solution

[0014] To achieve the above-mentioned objectives, the present invention provides the following technical solution: a method for optimizing energy and task scheduling in an edge computing system, comprising the following steps:

[0015] Step 1: Based on the new energy and task scheduling protocol, the MEC system can adaptively switch between energy harvesting mode, IRS auxiliary task offloading mode and IRS standby task offloading mode according to channel conditions, IRS battery energy status and user task queue status.

[0016] The second step is to model the system optimization problem based on the developed protocol, minimizing long-term user task offloading and computing energy consumption.

[0017] The third step is to use the Lyapunov optimization method to decompose it into a time-slot-based deterministic optimization problem, and then solve the corresponding deterministic optimization problem using convex optimization theory.

[0018] Preferably, the specific steps in the first step are as follows:

[0019] S1: Establish the channel model;

[0020] The channels in the MEC system are quasi-static channels;

[0021] The user can offload computing task data to HAP via UA link and URA link;

[0022] In a UA link, the channel coefficient in time slot k is represented as h. UA (k), and model it as Rayleigh fading, i.e. Where ρ0 is the path loss at the reference distance d0 = 1m, and α UA It is the path loss exponent for the UA channel link, d UA It is the distance between the user terminal and the HAP. It is a complex Gaussian random scattering component with zero mean and unit variance;

[0023] The URA link includes two channel links: user-to-IRS (UR) and IRS-to-HAP (RA). The channel coefficient vector in time slot k is uniformly represented as follows: Where ab∈{UR,RA}, α ab d is the channel path loss exponent from node a to node b. ab ζ is the distance between node a and node b. ab It is the Rice factor associated with small-scale fading. It is the ULA array response vector. Let I be a complex matrix with I rows and J columns. In the middle, φ ab (k) represents the arrival angle or departure angle of the corresponding signal, (·) T This is represented as a transpose operation. It is the non-direct component in the Ricean fading channel, where each element is a random scattering component with zero mean and unit variance.

[0024] set up Let θ represent the reflection vector of the IRS in time slot k, where θ n(k) is the phase shift of the nth reflecting element. For the reflection amplitude coefficient of each reflecting element, it is set to the maximum achievable value to maximize the signal reflection power. Therefore, the reflection coefficient of the IRS should satisfy the following constraints:

[0025]

[0026] S2: Wireless Power Supply IRS Auxiliary Task Offloading Protocol;

[0027] The MEC system under the new protocol can operate in energy harvesting mode, IRS auxiliary task offloading mode, and IRS standby task offloading mode, where t e (k) and t o (k) represents the duration of energy collection by the IRS and the duration of data offloading computing tasks to the HAP in a time slot k, respectively. T is the length of a time slot. In all three modes, the user will execute part of the computing tasks locally for the entire duration of the time slot, but the user's computing task offloading and energy collection by the IRS cannot be performed simultaneously.

[0028] In the time slot k The following equation holds: φ I (k)t e (k)+φ II (k)(t e (k)+t o (k))+φ III (k)t o (k) = T.

[0029] Preferably, in the energy harvesting mode, all time in a time slot is used for energy harvesting of the IRS. In this case, the HAP transmits RF energy signals to the IRS, and the IRS harvests energy from these RF energy signals. In this mode, the user terminal does not unload computing task data to the HAP, but only relies on itself to perform computing tasks locally.

[0030] In the IRS-assisted task offloading mode, a time slot is divided into two phases. In the first phase, the IRS performs energy harvesting; in the second phase, the user terminal, with the assistance of the IRS, offloads computational task data to the HAP. As a special case, in this mode, when the initial energy of the IRS is sufficient, the first phase may not exist. In this case, the IRS will assist the user terminal in offloading computational task data to the HAP throughout the entire time slot, i.e., t e =0 and t o =T;

[0031] In IRS standby task offloading mode, users offload computing task data to HAP only through the UA link, and the IRS is in a standby state with the power off. This mode will be selected in the following two situations: First, when the IRS battery power is insufficient, the IRS cannot participate in auxiliary task offloading; Second, when the UA link channel quality of the current time slot is good, users can directly offload computing tasks to HAP through the UA link.

[0032] Preferably, the specific steps of the second step are as follows:

[0033] S1: The user's energy consumption model, which includes the energy consumption of task unloading and the energy consumption of task local computation.

[0034] S2: Energy harvesting and consumption model of IRS;

[0035] In both energy harvesting mode and IRS auxiliary task offloading mode, the IRS harvests energy from the RF energy signal transmitted by the HAP. The energy harvested by the IRS in time slot k can be expressed as:

[0036] In IRS auxiliary task offloading mode, the energy consumed by the IRS in time slot k is E. C (k)=μNφ II (k)t o (k);

[0037] Preferably, the energy consumption of task unloading includes:

[0038] When running in IRS auxiliary task offload mode, the maximum achievable data transfer rate is:

[0039]

[0040] B is the system bandwidth, p(k) is the user's transmit power, and σ 2 This is the additive white Gaussian noise power at the HAP. Let d(k) be the power of t. o (k) The amount of task data unloaded during the period;

[0041] The energy consumption for the user to perform task unloading is:

[0042]

[0043] When the IRS standby task unloading mode is running, the energy consumed by the user terminal to unload the data of task d(k) is:

[0044]

[0045] S3: Problem Modeling. When processing computational tasks, the user client can schedule the amount of computational tasks in the task queue within a time period. At the beginning of time slot k, the user task queue state is represented as Q(k), and at the end of time slot k or the equivalent instant (k+1), the state is... - Let the user task queue state be represented as Q(k+1). The user performs local computation in all three modes, and performs task unloading in IRS auxiliary task unloading mode and IRS standby task unloading mode. Let D(k) be the amount of task data executed and unloaded locally by the user in time slot k, then we have...

[0046] Preferably, the specific steps of the third step are as follows:

[0047] S1: Define a virtual energy state based on the energy state B(k) of the IRS battery:

[0048] X(k) = B(k) - G;

[0049] S2: where G = 2TNμ is a time-independent constant, described as:

[0050] X(k+1)=X(k)+E H (k)-E C (k);

[0051] S3: Define the quadratic Lyapunov function as:

[0052]

[0053] S4: Introduce the Lyapunov drift function Δ(Ω(k)):

[0054]

[0055] S5: Further define the Lyapunov drift penalty function, which is obtained by weighting the Lyapunov drift function and the objective function of the deterministic optimization problem:

[0056]

[0057] Where λ is a non-negative weighting factor;

[0058] S6: Theorem: Upper bound of the Lyapunov drift penalty function:

[0059]

[0060] M is a finite constant independent of λ;

[0061]

[0062] S7: Rewrite the optimization objective from the problem's objective function into a Lyapunov drift penalty function. Using the upper bound of the drift penalty function, the original problem can be transformed into finding the minimum of that upper bound.

[0063]

[0064]

[0065] φ I (k)t e (k)+φ II (k)(t e (k)+t o (k))+φ III (k)t o (k)=T

[0066]

[0067] d(k)≥0, l(k)≥0, T≥τ(k)≥0;

[0068] S8: Based on problem-solving and system optimization algorithms, determine the optimal system working mode, thereby obtaining the optimal solution to the problem of minimizing the value;

[0069] When φ I When (k) = 1, the system operates in energy harvesting mode, and the minimum value problem can be simplified as:

[0070]

[0071] stl(k)≥0;

[0072] The objective function is O(k), for the equation By solving the problem and considering the constraint l(k)≥0, the optimal solution for the optimization variable l(k) can be obtained as follows:

[0073]

[0074] When φ II When Ψ'(k) = 1, the system operates in IRS auxiliary task offloading mode. Let Ψ'(k) = {d(k),l(k),t(k),Θ(k)}, then the minimum value problem can be rewritten as follows:

[0075]

[0076]

[0077] d(k)≥0, l(k)≥0, T≥τ(k)≥0;

[0078] S9: Due to Therefore, the optimal solution for the optimization variable Θ(k) can be obtained as follows:

[0079]

[0080] in

[0081] After obtaining l * (k) and θ * After (k), the problem can be simplified to the following:

[0082]

[0083] std(k)≥0,T≥τ(k)≥0;

[0084] S10, After solving the above problem and obtaining the optimal solution, Y can be determined. m The value of (k)(m∈{I,II,III}) can be used to determine the optimal system operating mode for the k-th time slot, as shown by the following formula:

[0085]

[0086] Preferably, the system optimization algorithm includes the following steps:

[0087] S1: Initialization: k = 1;

[0088] S2: while TRUE;

[0089] S3: Obtain the system channel state information (CSI) for the kth time slot, and read the energy state information B(k) of the IRS battery and the user task queue state information Q(k);

[0090] S4: Solve the optimization problems corresponding to the three modes, obtain the optimal solutions for d(k), l(k), t(k), and Θ(k), and calculate Y. m (k);

[0091] S5: Determine the system operating mode * (k);

[0092] S6: According to m * (k) and the optimal solutions of d(k), l(k), t(k) and Θ(k) in the corresponding system working mode, perform optimal resource allocation, and update the queue state B(k+1) and Q(k+1) of the next time slot;

[0093] S7: k = k + 1;

[0094] S8: end while.

[0095] (III) Beneficial Effects

[0096] Compared with existing technologies, this invention provides a method for optimizing energy and task scheduling in edge computing systems, which has the following beneficial effects:

[0097] 1. The proposed method for optimizing the energy and task scheduling of the edge computing system has the lowest energy consumption compared with four benchmark schemes. Specifically, compared with the short-sighted scheme, the system energy consumption of the proposed scheme is only 10%-50% of its energy consumption, and compared with the local computing scheme and the HAP-only computing scheme, the energy saving is even greater. Therefore, using the new protocol and system optimization algorithm proposed in this paper can significantly save energy consumption at the user end.

[0098] 2. The optimization method for energy and task scheduling in this edge computing system shows that when the path loss index increases from 2.5 to 5, the energy consumption of the scheme without IRS assistance increases by about 22 times, while the energy consumption of the scheme proposed in this paper only increases by about 2 times. This further verifies that deploying IRS in the system can significantly save energy consumption at the user end. At the same time, for the HAP-only computing scheme, when the path loss index increases from 2.5 to 5, the energy consumption increases by about 6 times, thus verifying that using the partial offloading method can save energy consumption at the user end. In addition, for all UA link path loss indices, the energy consumption performance of the scheme proposed in this paper is also significantly better than the short-sighted scheme. Therefore, it further verifies that using the new protocol and optimization algorithm proposed in this paper can achieve better energy consumption performance than the energy and task scheduling methods in references [2-3]. Attached Figure Description

[0099] Figure 1 Schematic diagram of a wireless-powered IRS-assisted MEC system;

[0100] Figure 2 A schematic diagram of the three system operation modes in the proposed task unloading protocol;

[0101] Figure 3 This is a schematic diagram comparing the energy consumption performance of different schemes when the HAP transmit power changes;

[0102] Figure 4 This diagram illustrates the energy consumption performance comparison of different schemes when the UA link channel quality changes.

[0103] Figure 5 This is a schematic diagram of the system optimization algorithm process. Detailed Implementation

[0104] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0105] Considering Figure 1 In the wirelessly powered IRS-assisted MEC system shown, the computational tasks to be performed arrive randomly at the user end. Due to the limited computing power of the user end itself, some computational tasks need to be offloaded to the HAP for collaborative computation. Simultaneously, it is assumed that there are obstacles between the user end and the HAP, resulting in poor channel link quality between the user end and the HAP (UA). Therefore, an IRS needs to be deployed between the two to improve the performance of offloading computational tasks at the user end. In other words, the HAP can simultaneously receive task data from the user end through both the UA link and the URA (user→IRS→HAP) link. This paper assumes that the IRS consists of a uniform linear array (ULA) with N reflective elements, a controller that can adjust the phase shift of each reflective element, a radio frequency energy harvesting circuit, and a rechargeable battery. The IRS collects the radio frequency signal energy emitted from the HAP through the radio frequency energy harvesting circuit, stores it in the rechargeable battery, and then uses this stored energy for signal reflection. Furthermore, since the transmit power of the user end is usually much lower than that of the HAP, this paper ignores the energy harvested by the IRS from the signal emitted by the user end.

[0106] In the considered MEC system, assume the user task arrival and execution model is described below. Assume the system operates based on time slots, and consider time periods of length K*T, where K is the number of time slots and T is the length of each time slot. In each time slot... Initially, new computation tasks arrive at the client, and these tasks are cached in the client's computation task buffer queue. The client processes these tasks according to a FIFO (First-In, First-Out) approach. Let the size of the computation task data arriving at the client in each time slot be denoted as A(k)≥0, and assume it follows a mean of Ak. mean =A max A uniform distribution of / 2, i.e. Where A max This represents the maximum amount of computational tasks arriving in each time slot. For ease of analysis, this paper assumes that the length of the user-side computational task buffer queue is infinite; however, in subsequent simulations, it will be verified that the required queue length will not exceed an upper bound. Therefore, the algorithm designed in this paper can also be applied to cases where the user queue buffer capacity is finite.

[0107] An optimization method for energy and task scheduling in an edge computing system includes the following steps:

[0108] S1. In the wireless power supply IRS-assisted MEC system studied in this paper, in order to increase the energy collected by the IRS and utilize the collected energy efficiently, thereby improving the system performance, a new energy and task scheduling protocol is proposed. This protocol enables the MEC system to adaptively switch between three modes (i.e., energy collection mode, IRS-assisted task offloading mode, and IRS standby task offloading mode) according to channel conditions, IRS battery energy status, and user task queue status.

[0109] Specifically, step S1 includes the following steps:

[0110] S11, Channel Model

[0111] This paper assumes that the channels in the MEC system are quasi-static channels, meaning they remain unchanged within a single time slot but can vary independently across different time slots. Furthermore, each task offloading from the user terminal to the HAP is completed within a separate time slot. In other words, at the beginning of each time slot, the user terminal will decide whether and how to offload its computational task data to the HAP.

[0112] As described in the previous section, the user terminal can offload computational task data to the HAP via the UA link and the URA link. For the UA link, the channel coefficients in time slot k are represented as h. UA (k), and model it as Rayleigh fading, i.e. Where ρ0 is the path loss at the reference distance d0 = 1m, and α UA It is the path loss exponent for the UA channel link, d UA It is the distance between the user terminal and the HAP. It is a complex Gaussian random scattering component with zero mean and unit variance. For a URA link, including two channel links: user-to-IRS (UR) and IRS-to-HAP (RA), the channel coefficient vector in time slot k is uniformly represented as... Where ab∈{UR,RA}, α ab d is the channel path loss exponent from node a to node b. ab ζ is the distance between node a and node b. ab It is the Rice factor associated with small-scale fading. It is the ULA array response vector. A complex matrix with I rows and J columns; in In the middle, φ ab (k) represents the arrival angle or departure angle of the corresponding signal, (·) TThis is represented as a transpose operation. It is the non-direct component in the Ricean fading channel, where each element is a random scattering component with zero mean and unit variance.

[0113] In addition, Let θ represent the reflection vector of the IRS in time slot k, where θ n (k) is the phase shift of the nth reflecting element. The reflection amplitude coefficient of each reflecting element is set to the maximum achievable value to maximize the signal reflection power. Therefore, the reflection coefficient of the IRS should satisfy the following constraints:

[0114]

[0115] In practical applications, the phase shift of an IRS is usually a discrete value. However, to simplify the analysis, this paper adopts the assumption common to most current IRS-related studies, namely, that the reflection phase shift of an IRS is continuous.

[0116] Since the URA link is obtained by cascading the UR link, the IRS reflection phase shift, and the RA link, the channel coefficient of the URA link in time slot k can be expressed as: Where Θ(k) is a diagonal matrix, i.e., Θ(k) = diag(θ(k)). Therefore, in time slot k, when the user offloads computational task data to the HAP via the UA and URA links, the offloading equivalent combined channel coefficients can be expressed as:

[0117] As mentioned earlier, the IRS harvests energy from the RF signal transmitted from the HAP. Considering hardware implementation feasibility and cost factors, this paper assumes that the IRS uses a single antenna independent of the reflecting element for energy harvesting. In time slot k, the link channel coefficient from HAP to IRS (AR, HAP-to-IRS) is denoted as g. AR (k), which follows a Rice distribution, i.e. Where α AR It is the corresponding path loss exponent for the AR link, d AR Indicates the distance between HAP and IRS. This represents the random scattering component.

[0118] S12, Wireless Power Supply IRS Auxiliary Task Offload Protocol

[0119] To effectively utilize the time-varying nature of wireless channels for energy harvesting and to efficiently use the harvested energy, this paper proposes a novel task offloading protocol for wirelessly powered IRS-assisted MEC systems. In references [2-3], the IRS must use up all available energy at the end of each time slot, and user-generated computational tasks must be completed within a single time slot. In contrast, the proposed protocol allows the IRS to adaptively schedule energy and tasks based on the channel quality of the system link, the energy state of the IRS battery, and the user task queue status. Specifically, the MEC system under the new protocol can... Figure 2 The three modes shown (i.e., energy harvesting mode, IRS auxiliary task offloading mode, and IRS standby task offloading mode) are operated, where t e (k) and t o (k) represents the duration of energy collection by the IRS and the duration of data offloading from the computing task to the HAP within a time slot k, respectively, where T is the length of a time slot. For ease of description, let's use... Figure 2 The three modes in (a)-(c) are denoted as Mode I, Mode II, and Mode III, respectively. Figure 2 In the three modes shown, users will perform part of the computational tasks locally for the entire duration of the time slot, but the user's computational task offloading and IRS energy harvesting cannot occur simultaneously.

[0120] In Mode I, all time in a time slot is dedicated to energy harvesting from the IRS. In this mode, the HAP transmits RF energy signals to the IRS, and the IRS harvests energy from these RF signals. Simultaneously, in this mode, the user terminal does not offload computational task data to the HAP; it executes computational tasks locally.

[0121] In Mode II, a time slot is divided into two phases. In the first phase, the IRS performs energy harvesting; in the second phase, the user terminal, with the assistance of the IRS, offloads computational task data to the HAP. As a special case, in this mode, if the IRS has sufficient initial energy, the first phase may not exist; in this case, the IRS will assist the user terminal in offloading computational task data to the HAP throughout the entire time slot, i.e., t e =0 and t o =T.

[0122] In Mode III, users offload computational task data to the HAP only via the UA link, while the IRS remains in standby mode with its power off. This mode is selected in the following two situations: first, when the IRS battery is low, the IRS cannot participate in auxiliary task offloading; second, when the UA link channel quality in the current time slot is good, users can directly offload computational tasks to the HAP via the UA link, thereby saving IRS energy for use in subsequent time slots.

[0123] Let the set of the above three MEC system operating modes be denoted as . Let φ m (k)∈{0,1} serves as the working mode indicator, where When φ m When (k) = 1, the MEC system operates in mode m in time slot k. Within a time slot, the system can only select one operating mode; therefore, we have...

[0124] according to Figure 2 When the MEC system is operating in Mode I, t e (k) = T, t o (k) = 0; when the MEC system is operating in Mode II, t e (k)=T-τ(k),t o (k)=τ(k); When the MEC system is operating in Mode III, t e (k)=0, t o (k) = T. Therefore, in time slot k, the following equation holds:

[0125] φ I (k)t e (k)+φ II (k)(t e (k)+t o (k))+φ III (k)t o (k)=T (2)

[0126] Generally, the execution of computing tasks by a user terminal through an MEC server involves three stages: task unloading, remote execution, and result download. Since the time for remote execution and result download is typically much shorter than the time for task unloading, this paper will ignore these two stages and focus on the first stage, task unloading. For many compute-intensive IoT applications (e.g., image / video / speech recognition, document scanning, data analysis, multi-sensor information processing), this assumption is reasonable because the MEC server deployed in the HAP usually has more computing resources than the user terminal, and the amount of computational result data is typically much smaller than the amount of task input data.

[0127] S2. Based on the developed protocol, the system optimization problem was modeled to minimize long-term user task offloading and computing energy consumption;

[0128] Specifically, step S2 includes the following steps:

[0129] S21, User's Energy Consumption Model

[0130] 1) Energy consumption for task offloading: According to the relevant protocols described in the previous section, when the MEC system is running in Mode II, the user terminal can offload task data to the HAP via the UA and URA links. The maximum achievable data transfer rate is...

[0131]

[0132] Where B is the system bandwidth, p(k) is the user's transmit power, and σ 2 This is the additive white Gaussian noise power at the HAP. Let d(k) be the power of t. o (k) is the amount of task data unloaded during this period. Therefore, the energy consumption for the client to perform task unloading in this mode can be calculated as follows:

[0133]

[0134] When the MEC system is running in Mode III, the user only offloads task data to the HAP via the UA link. Therefore, similar to the derivation in (4), the energy consumed by the user to offload the amount of task data d(k) in Mode III is:

[0135]

[0136] 2) Energy Consumption of Local Computation: Let C≥0 be the number of CPU cycles required for the user terminal to execute one computation task bit. This number typically depends on the type of computation task and the CPU architecture of the user terminal. Furthermore, let l(k) represent the task input bit for local computation performed by the user terminal in time slot k. It can be proven that, to save energy, the user terminal should employ dynamic voltage and frequency scaling techniques to perform local computation in time slot k at a constant CPU frequency Cl(k) / T. Therefore, the energy consumption of the user terminal performing local computation in time slot k can be expressed as...

[0137]

[0138] Where ζ>0 represents the effective switching capacitor coefficient, which depends on the CPU chip architecture of the user end.

[0139] Based on the above analysis, the total energy consumption of the user terminal in time slot k can be expressed as:

[0140]

[0141] S22, IRS Energy Harvesting and Consumption Model

[0142] like Figure 2As shown, the IRS harvests energy from the RF energy signal emitted by the HAP in both Mode I and Mode II. Let η∈(0,1) represent the energy harvesting efficiency, and P A Let represent the transmit power of the HAP. Therefore, the energy collected by the IRS in time slot k can be expressed as:

[0143] Furthermore, in Mode II, the IRS consumes energy while assisting the user in reflecting computational task data signals to the HAP. Typically, the power consumption of the IRS increases linearly with its size and depends on the phase resolution of a single reflective element. Let μ represent the power consumption of a single reflective element, which is related to the phase resolution. Therefore, the energy consumed by the IRS in time slot k can be obtained as E. C (k)=μNφ II (k)t o (k).

[0144] S23, Problem Modeling

[0145] As mentioned earlier, when processing computational tasks, the client can schedule the amount of computational tasks in the task queue within a time period. At the beginning of time slot k (denoted as time instant k)... - The user task queue state (i.e., the number of bits stored in the user-side computation task data buffer) is represented as Q(k); at the end of time slot k or the equivalent instant (k+1). - The user task queue state is represented as Q(k+1). According to... Figure 2 The protocol shown allows users to perform local computation in all three modes, with task offloading in modes II and III. Let D(k) be the amount of task data executed and offloaded locally by the user in time slot k, then we have... Furthermore, at the beginning of time slot k, a new computational task arrives at the user end, denoted by its size A(k). Therefore, the changes in the user task queue state should satisfy the following equation:

[0146] Q(k+1)=max{Q(k)+A(k)-D(k),0} (8)

[0147] Meanwhile, stability is an important indicator of a user's task queue buffer; it means that the average number of tasks executed should not exceed the average task arrival rate over time.

[0148]

[0149] Similar to Q(k), the energy state of the IRS battery at the start of time slot k is represented as B(k) ≥ 0. According to the aforementioned task offloading protocol, at the end of time slot k, the IRS battery may have some remaining energy for use in the next time slot (k+1). Therefore, at the end of time slot k (i.e., at the instant of time (k+1)... - The energy state of an IRS cell is expressed as B(k+1)≥0. Therefore, the energy state evolution of an IRS cell should satisfy the following equation:

[0150] B(k+1)=B(k)+E H (k)-E C (k) (10)

[0151] At the same time, the average energy consumed by the IRS over a long time period should not exceed the average energy collected, i.e.

[0152]

[0153] for Figure 1 The wirelessly powered IRS-assisted MEC system shown in this paper aims to optimize the system operating mode for each time slot, user task scheduling, IRS reflection phase shift and time allocation in Mode II (i.e., Ψ(k)={Φ(k),d(k),l(k),t(k),Θ(k)}, where Φ(k)={φ I (k),φ II (k),φ III (k)},t(k)={t e (k),t o (k)}), minimizing the average energy consumption of the user end for task computation and unloading, i.e. Based on the IRS reflection coefficient constraint in (1), the time allocation constraint in (2), the long-term average task scheduling constraint in (9), and the long-term average energy scheduling constraint in (11), the energy minimization problem studied in this paper can be expressed as follows:

[0154]

[0155]

[0156] C2:φ I (k)t e (k)+φ II (k)(t e (k)+t o (k))

[0157] +φ III (k)t o (k)=T

[0158]

[0159]

[0160]

[0161] C6:d(k)≥0,l(k)≥0,T≥τ(k)≥0 (12)

[0162] In problem (12), since the wireless channels and the amount of incoming tasks in each time slot are random, the channel state information and task state information for subsequent time slots (i.e., time slots k+1, k+2, ...) cannot be determined in time slot k. Therefore, problem (12) is a classic stochastic optimization problem that is difficult to solve directly. To solve this problem, this paper decomposes it into a series of deterministic optimization problems that are independent of each other in time slots based on the Lyapunov optimization method, and solves the corresponding deterministic optimization problems through convex optimization theory, thereby proposing a low-complexity and efficient algorithm.

[0163] S3. Using the Lyapunov optimization method, the problem is decomposed into a time-slot-based deterministic optimization problem, and the corresponding deterministic optimization problem is solved by convex optimization theory, thus proposing a low-complexity and efficient online algorithm.

[0164] Specifically, step S3 includes the following steps:

[0165] S31, Problem Transformation

[0166] In order to solve problem (12) using the Lyapunov optimization method, a virtual energy state is first defined based on the energy state B(k) of the IRS cell:

[0167] X(k)=B(k)-G (13)

[0168] Where G = 2TNμ is a time-independent constant. From equation (13), it can be seen that although B(k) ≥ 0, X(k) can take negative values. According to equation (10), the state change of X(k) can be described as...

[0169] X(k+1)=X(k)+E H (k)-E C (k) (14)

[0170] In the literature, it has been proven that ensuring the stability of queue X(k) is equivalent to satisfying the long-term average energy scheduling constraint C4 in problem (12).

[0171] Based on Q(k) and X(k), let Ω(k) = [Q(k), X(k)] be a generalized queue. Therefore, the quadratic Lyapunov function can be defined as follows:

[0172]

[0173] Here, v is a non-negative constant that ensures that the values ​​of Q(k) and X(k) are of the same order of magnitude. Furthermore, to guarantee the stability of the generalized queue Ω(k), a Lyapunov drift function Δ(Ω(k)) is introduced:

[0174]

[0175] It reflects the change in the generalized queue Ω(k) from time slot k to time slot (k+1).

[0176] Based on Lyapunov optimization theory, a Lyapunov drift penalty function can be further defined, which is obtained by weighting the Lyapunov drift function and the objective function of problem (12), i.e.

[0177]

[0178] Where λ is a non-negative weighting factor.

[0179] To further simplify the optimization problem, the following theorem gives an upper bound for the Lyapunov drift penalty function.

[0180] The upper bound of the Lyapunov drift penalty function for each time slot can be determined by the following expression.

[0181]

[0182] Where M is a finite constant independent of λ, it can be written as

[0183]

[0184] According to the Lyapunov optimization method, the optimization objective can be rewritten from the objective function of problem (12) to the Lyapunov drift penalty function, thereby minimizing system energy consumption while ensuring system queue stability. Furthermore, by utilizing the upper bound of the drift penalty function in equation (18), the original problem can be transformed into a problem of finding the minimum value of this upper bound, i.e.

[0185]

[0186]

[0187] φ I (k)t e (k)+φ II (k)(t e (k)+t o (k))+φ III (k)t o(k)=T

[0188]

[0189] d(k)≥0,l(k)≥0,T≥τ(k)≥0 (20)

[0190] Compared to problem (12), which requires solving optimization variables for multiple time slots, problem (20) only involves solving optimization variables for one time slot (i.e., the kth time slot), so this problem is relatively easy to handle.

[0191] S32, Problem Solving and System Optimization Algorithms

[0192] To solve problem (20), note that the system operating mode indicator φ(k) is a binary optimization variable. However, since there are only three system operating modes, the optimal system operating mode can be determined by solving the corresponding optimization problems under the three system operating modes respectively, thereby obtaining the optimal solution to problem (20).

[0193] When φ I When (k) = 1, the system operates in energy harvesting mode, and problem (20) can be simplified as follows:

[0194]

[0195] stl(k)≥0 (21)

[0196] Let the objective function of problem (21) be O(k). For the equation... Solving this problem, and considering the constraint l(k)≥0, we can obtain the optimal solution for the optimization variable l(k) as follows:

[0197]

[0198] When φ II When (k) = 1, the system operates in IRS auxiliary task offloading mode. Let Ψ'(k) = {d(k),l(k),t(k),Θ(k)}, then problem (20) can be rewritten as

[0199]

[0200]

[0201] d(k)≥0,l(k)≥0,T≥τ(k)≥0 (23)

[0202] Similar to the method for finding the optimal solution of l(k) in equation (22), the optimal solution of l(k) in problem (23) can be obtained. Furthermore, note that the optimal solution of the optimization variable Θ(k) can be obtained by maximizing... Obtained. Due to Therefore, the optimal solution for optimizing variable Θ(k) can be obtained as follows:

[0203]

[0204] in

[0205] After obtaining l * (k) and θ * After (k), problem (23) can be simplified to the following problem:

[0206]

[0207] std(k)≥0,T≥τ(k)≥0 (25)

[0208] To solve problem (25), we will discuss the following two cases:

[0209] ① When X(k)≥0, the optimal solution for the optimization variable τ(k) can be derived as follows:

[0210] τ * (k)=T (26)

[0211] Based on equation (26), the optimal solution for the optimization variable d(k) can be obtained as follows:

[0212]

[0213] ② When X(k) < 0, introduce a slack variable. Therefore, problem (25) can be rewritten as

[0214]

[0215] std(k)≥0,T≥τ(k)≥0

[0216] d(k)log(2)≤-τ(k)Blog2(τ(k)B / z) (28)

[0217] It can be proven that problem (28) is a convex problem. Therefore, the optimal solution to this problem can be obtained by the interior point method.

[0218] When φ III When (k) = 1, the system operates in IRS standby task offload mode. Therefore, problem (20) can be rewritten as follows:

[0219]

[0220] std(k)≥0, l(k)≥0 (29)

[0221] Similar to the method of finding the optimal solutions for l(k) and d(k) in equations (22) and (25), the optimal solutions for l(k) and d(k) in problem (29) can be obtained.

[0222] After obtaining the optimal solutions to problems (21), (23), and (29), Y can be determined. m The value of (k)(m∈{I,II,III}) can be used to determine the optimal system operating mode for the k-th time slot, as shown by the following formula:

[0223]

[0224] In summary, the system optimization algorithm is shown in Algorithm 1.

[0225] System optimization algorithms based on Lyapunov optimization theory include the following steps:

[0226] 1) Initialization: k = 1;

[0227] 2) while TRUE;

[0228] 3) Obtain the system channel state information (CSI) for the kth time slot, and read the energy state information B(k) of the IRS battery and the user task queue state information Q(k);

[0229] 4) Solve the optimization problems (21), (23) and (30) corresponding to the three modes to obtain the optimal solutions of d(k), l(k), t(k) and Θ(k), and calculate Y. m (k);

[0230] 5) Determine the system operating mode m * (k);

[0231] 6) According to m * (k) and the optimal solutions of d(k), l(k), t(k) and Θ(k) in the corresponding system working mode, perform optimal resource allocation, and update the queue state B(k+1) and Q(k+1) of the next time slot according to equations (8) and (10);

[0232] 7) k = k + 1;

[0233] 8) end while.

[0234] Figure 3 The graph shows the transmit power of the HAP (i.e., P). A The energy consumption performance of the proposed scheme and four benchmark schemes changes when the energy consumption changes. Figure 3As can be seen, the proposed scheme has the lowest energy consumption compared to the four benchmark schemes. Specifically, compared to the short-sighted scheme, the proposed scheme consumes only 10%-50% of its energy; and compared to the local computing scheme and the HAP-only computing scheme, the energy savings are even greater. Therefore, using the new protocol and system optimization algorithm proposed in this paper can significantly reduce the energy consumption at the user end. Furthermore, compared to the scheme without IRS assistance, it can be found that when P... A Smaller (e.g., P) A When P = 10dBm, the proposed scheme has essentially the same energy consumption performance. This is because, in this scenario, the IRS needs to spend most of its time harvesting energy to support its operation, thus limiting its role in assisting users with task offloading. However, when P... A When the energy consumption is 30dBm, the proposed solution consumes only 22.66% of the energy consumption of the solution without IRS assistance, which demonstrates that deploying IRS in the system can significantly reduce user-side energy consumption.

[0235] Figure 4 The impact of UA link channel quality on the energy consumption performance of different schemes is plotted. From Figure 4 It can be seen that for the proposed scheme, the scheme without IRS assistance, the short-term scheme, and the HAP-only scheme, all of which employ task offloading, their energy consumption increases with the increase of the UA link path loss index. In particular, when the path loss index increases from 2.5 to 5, the energy consumption of the scheme without IRS assistance increases by about 22 times, while the energy consumption of the proposed scheme only increases by about 2 times, thus further verifying that deploying IRS in the system can significantly save user-end energy consumption. At the same time, for the HAP-only scheme, when the path loss index increases from 2.5 to 5, the energy consumption increases by about 6 times, thus verifying that using partial offloading can save user-end energy consumption. In addition, for all UA link path loss indices, the energy consumption performance of the proposed scheme is significantly better than that of the short-term scheme, thus further verifying that using the new protocol and optimization algorithm proposed in this paper can achieve better energy consumption performance than the energy and task scheduling methods in references [2-3].

[0236] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing energy and task scheduling in an edge computing system, characterized in that, Includes the following steps: Step 1: Based on the new energy and task scheduling protocol, the MEC system can adaptively switch between energy harvesting mode, IRS auxiliary task offloading mode and IRS standby task offloading mode according to channel conditions, IRS battery energy status and user task queue status. The second step is to model the system optimization problem based on the developed protocol, minimizing long-term user task offloading and computing energy consumption. Step 3: Using the Lyapunov optimization method, decompose it into a time-slot-based deterministic optimization problem, and solve the corresponding deterministic optimization problem using convex optimization theory; The specific steps of the third step are as follows: S1: Define a virtual energy state based on the energy state B(k) of the IRS battery: X(k) = B(k) - G; S2: where G = 2TNμ is a time-independent constant, described as: X(k+1)=X(k)+E H (k)-E C (k); S3: Define the quadratic Lyapunov function as: S4: Introduce the Lyapunov drift function Δ(Ω(k)): S5: Further define the Lyapunov drift penalty function, which is obtained by weighting the Lyapunov drift function and the objective function of the deterministic optimization problem: Where λ is a non-negative weighting factor; S6: Theorem: Upper bound of the Lyapunov drift penalty function: M is a finite constant independent of λ; S7: Rewrite the optimization objective from the problem's objective function into a Lyapunov drift penalty function. Using the upper bound of the drift penalty function, the original problem can be transformed into finding the minimum of that upper bound. d(k)≥0, l(k)≥0, T≥τ(k)≥0; S8: Based on problem-solving and system optimization algorithms, determine the optimal system working mode, thereby obtaining the optimal solution to the problem of minimizing the value; When φ Ι When (k) = 1, the system operates in energy harvesting mode, and the minimum problem can be simplified as: stl(k)≥0; The objective function is O(k), for the equation By solving the problem and considering the constraint l(k)≥0, the optimal solution for the optimization variable l(k) can be obtained as follows: When φ ΙΙ When Ψ'(k) = 1, the system operates in IRS auxiliary task offloading mode. Let Ψ'(k) = {d(k),l(k),t(k),Θ(k)}, then the minimum value problem can be rewritten as: d(k)≥0, l(k)≥0, T≥τ(k)≥0; S9: Due to Therefore, the optimal solution for optimizing variable Θ(k) can be obtained as follows: in After obtaining l * (k) and θ * After (k), the problem can be simplified to the following: std(k)≥0,T≥τ(k)≥0; S10, After solving the above problem and obtaining the optimal solution, Y can be determined. m The value of (k)(m∈{I,II,III}) can be used to determine the optimal system operating mode for the k-th time slot, as shown by the following formula: ① When X(k)≥0, the optimal solution for the optimization variable τ(k) can be derived as follows: t * (k)=T (26) Based on equation (26), the optimal solution for the optimization variable d(k) can be obtained as follows: ② When X(k) < 0, introduce a slack variable. Therefore, problem (25) can be rewritten as std(k)≥0,T≥τ(k)≥0 d(k)log(2)≤-τ(k)Blog2(τ(k)B / z) (28) It can be proven that problem (28) is a convex problem; therefore, the optimal solution to the problem can be obtained by the interior point method.

2. The method for optimizing energy and task scheduling in an edge computing system according to claim 1, characterized in that: The specific steps in the first step are as follows: S1: Establish the channel model; The channels in the MEC system are quasi-static channels; The user can offload computing task data to HAP via UA link and URA link; In a UA link, the channel coefficient in time slot k is represented as h. UA (k), and model it as Rayleigh fading, i.e. Where ρ0 is the path loss at the reference distance d0 = 1m, and α UA It is the path loss exponent for the UA channel link, d UA It is the distance between the user terminal and the HAP. It is a complex Gaussian random scattering component with zero mean and unit variance; The URA link includes two channel links: user-to-IRS (UR) and IRS-to-HAP (RA). The channel coefficient vector in time slot k is uniformly represented as follows: Where ab∈{UR,RA}, α ab d is the channel path loss exponent from node a to node b. ab ζ is the distance between node a and node b. ab It is the Rice factor associated with small-scale fading. It is the ULA array response vector. Let I be a complex matrix with I rows and J columns. In the middle, φ ab (k) represents the arrival angle or departure angle of the corresponding signal, (·) T This is represented as a transpose operation. It is the non-direct component in the Ricean fading channel, where each element is a random scattering component with zero mean and unit variance. set up Let θ represent the reflection vector of the IRS in time slot k, where θ n (k) is the phase shift of the nth reflecting element. For the reflection amplitude coefficient of each reflecting element, it is set to the maximum achievable value to maximize the signal reflection power. Therefore, the reflection coefficient of the IRS should satisfy the following constraints: S2: Wireless Power Supply IRS Auxiliary Task Offloading Protocol; The MEC system under the new protocol can operate in energy harvesting mode, IRS auxiliary task offloading mode, and IRS standby task offloading mode, where t e (k) and t o (k) represents the duration of energy collection by the IRS and the duration of data offloading computing tasks to the HAP in a time slot k, respectively. T is the length of a time slot. In all three modes, the user will execute part of the computing tasks locally for the entire duration of the time slot, but the user's computing task offloading and energy collection by the IRS cannot be performed simultaneously. In time slot k, the following equation holds: φ I (k)t e (k)+φ II (k)(t e (k)+t o (k))+φ III (k)t o (k) = T.

3. The method for optimizing energy and task scheduling in an edge computing system according to claim 2, characterized in that: In the energy harvesting mode, all time in a time slot is used for energy harvesting from the IRS. In this case, the HAP transmits RF energy signals to the IRS, and the IRS harvests energy from these RF energy signals. In this mode, the user terminal does not unload computing task data to the HAP, but only relies on itself to perform computing tasks locally. In the IRS auxiliary task offloading mode, a time slot is divided into two phases. In the first phase, the IRS performs energy harvesting. In the second phase, with the assistance of the IRS, the user terminal offloads computational task data to the HAP. As a special case, in this mode, when the initial energy of the IRS is sufficient, the first phase may not exist. In this case, the IRS will assist the user terminal in offloading computational task data to the HAP throughout the entire time slot, i.e., t e =0 and t o =T; In IRS standby task offloading mode, users offload computing task data to HAP only through the UA link, and the IRS is in a standby state with the power off. This mode will be selected in the following two situations: First, when the IRS battery power is insufficient, the IRS cannot participate in auxiliary task offloading; Second, when the UA link channel quality of the current time slot is good, users can directly offload computing tasks to HAP through the UA link.

4. The method for optimizing energy and task scheduling in an edge computing system according to claim 1, characterized in that: The specific steps of the second step are as follows: S1: The user's energy consumption model, which includes the energy consumption of task unloading and the energy consumption of task local computation. S2: Energy harvesting and consumption model of IRS; In both energy harvesting mode and IRS auxiliary task offloading mode, the IRS harvests energy from the RF energy signal transmitted by the HAP. The energy harvested by the IRS in time slot k can be expressed as: In IRS auxiliary task offloading mode, the energy consumed by the IRS in time slot k is E. C (k)=μNφ II (k)t o (k).

5. The method for optimizing energy and task scheduling in an edge computing system according to claim 4, characterized in that: The energy consumption of the task unloading includes: When running in IRS auxiliary task offload mode, the maximum achievable data transfer rate is: B is the system bandwidth, p(k) is the user's transmit power, and σ 2 This is the additive white Gaussian noise power at the HAP. Let d(k) be the power of t. o (k) The amount of task data unloaded during the period; The energy consumption for the user to perform task unloading is: When the IRS standby task unloading mode is running, the energy consumed by the user terminal to unload the data of task d(k) is: S3: Problem Modeling. When processing computational tasks, the user client can schedule the amount of computational tasks in the task queue within a time period. At the beginning of time slot k, the state of the user task queue is represented as Q(k), and at the end of time slot k or the equivalent instant (k+1), the state is... - Let the user task queue state be represented as Q(k+1). The user performs local computation in all three modes, and performs task unloading in IRS auxiliary task unloading mode and IRS standby task unloading mode. Let D(k) be the amount of task data executed and unloaded locally by the user in time slot k, then we have...

6. The method for optimizing energy and task scheduling in an edge computing system according to claim 1, characterized in that: The system optimization algorithm includes the following steps: S1: Initialization: k = 1; S2: while TRUE; S3: Obtain the system channel state information (CSI) for the kth time slot, and read the energy state information B(k) of the IRS battery and the user task queue state information Q(k); S4: Solve the optimization problems corresponding to the three modes, obtain the optimal solutions for d(k), l(k), t(k), and Θ(k), and calculate Y. m (k); S5: Determine the system operating mode * (k); S6: According to m * (k) and the optimal solutions of d(k), l(k), t(k) and Θ(k) in the corresponding system working mode, perform optimal resource allocation, and update the queue state B(k+1) and Q(k+1) of the next time slot; S7: k = k + 1; S8: end while.

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